Question

A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

Answer 1

Explicit formula:
`s_(n)=6(2)^(n-1)`

Explanation:

Let the number of squares in
`n^(th)` layer be
`s_(n)`

Given:

Number of squares in first layer,
`s_(1)=6`

Number of squares in second layer,
`s_(2)=12`

Therefore, the number of squares increases by a factor of 2.

So, it follows a geometric sequence with the first term as 6 and common ratio of 2.

For a geometric sequence, the
`n^(th)` term with common ratio
`r` is given as:

`s_(n)=s_(1)* r^(n-1)`

Here,
`r=2,s_(1)=6`

∴ Explicit formula:
`s_(n)=6(2)^(n-1)`